The present invention relates to cable fault measurements, and more particularly to a method of cable loss correction of distance to fault (DTF) and of time domain reflectometer (TDR) measurements.
To explore the characteristics of a DTF measurement system an idealized impulse response is considered. Referring now to FIG. 1 a return loss bridge is coupled to a length of cable. The cable is open-circuited at the far end, giving a reflection coefficient ┌=1 at distance d. If the cable""s loss is neglected, the system""s impulse response and its Fourier transform may be written virtually by inspection. The impulse enters the cable via the return loss bridge and travels distance, d, to the end where it is reflected with a reflection coefficient, ┌. The impulse travels back along the cable and is routed to a measurement receiver by the return loss bridge. The system""s impulse response is simply ┌(t) convolved with a delay corresponding to 2d, i.e.,
g(xcex4)=┌(t)*xcex4(txe2x88x922d/(vrelc))
where ┌(t) is the reflection coefficient the signal sees at the end of the cable, d is the length of the cable, vrel is the relative velocity of the signal in the cable with respect to the speed of light, and c is the speed of light.
The Fourier transform of g(xcex4) is straight forward. ┌(t) transforms to ┌(f), the convolution, ┌*xcex4, transforms to a product, the impulse, xcex4(t), transforms to a unity value and the delay operator, xe2x88x922d/(vrelc), in the impulse""s argument transforms to an exponential that causes a phase change with frequency:
G(f)=┌(f)excex1f where xcex1=xe2x88x92j(4xcfx80d/vrelc).
But the cable is lossy. The function G(f) needs to be modified to account for the loss by adding the loss term associated with the two way travel in the cable:
G(f)=┌(f)L(d,f)excex1
To this point a cable system with only one reflection has been assumed. In actual measurements most cable systems have multiple sources of reflections. Treating each return arriving at the input terminals as a real signal regardless of whether it is real or is caused by the reflection of a reflection:
g(xcex4)=xcexa3n┌n(t)*xcex4(txe2x88x922d/vrelc), G(f)=xcexa3n┌n(f)excex1xe2x80x2f and G(f)=xcexa3n┌n(f)L(dn,f)excex1xe2x80x2
where xcex1xe2x80x2=xe2x88x92j(4xcfx80dn/vrelc)
This corresponds to the actual data created in a DTF measurement. This data is then windowed and passed through an inverse Fourier transform to determine the cable""s impulse response:
g(t)=ℑ1(G(f))
The inverse Fourier transform determines the distance of the various responses G(f) by grouping all portions of the signal together that have the same rate of change of phase as a function of frequency.
For the cable shown in FIG. 2 assume that G(f) has been determined by making measurements at every xcex94F in frequency, where xcex94F is 1.5 MHz, over a range of frequencies from Fstart to Fstop (25-3000 MHz) using an idealized, zero-loss cable. After the data is measured, it is windowed and then transformed into the time domain using a Fourier transformation. The result is shown in FIG. 3. The resistor between the two line sections and an open or short circuit at the end of the second section gives a theoretical response of two equal return loss responses, one at d1 and the other at d2. However, the actual result is different as the cable has loss. The sine wave test signal of a DTF process travels much further to the far end of the cable than to the resistor. Further where a low frequency test signal is used, the loss at either distance is fairly low. When a frequency near its upper end is used, the loss to the cable""s distant end is much greater than that from the resistor. The approximate result Is shown in FIG. 4 where d2""s response is smaller than the one from d1. Due to the smaller amplitude of the response at d2, the reflection may not be deemed to be significant.
The data in FIG. 4 is computed as a discrete signal, i.e., it is a vector or list of values, each defined as the arithmetic, complex value of the reflection, ┌d, at a distance d. ┌d is the cable system""s impulse response for whatever discontinuity is present at distance d, so the measured frequency response of this point alone is:
Gm(f)=┌dexcex1f
The frequency response of the entire DTF response may then be written as the summation of the effects of each point in turn:
Gm(f)=xcexa3d┌dexcex1f.
What is desired is a method of performing cable loss correction of distance to fault and of time domain reflectometry measurements so that DTF data is presented in the form of a lossless cable.
Accordingly the present invention provides a cable loss correction of distance to fault and time domain reflectrometry measurements by inserting a loss compensation factor, Lc, into the initial distance to fault calculation. Data acquired in the frequency domain is Fourier transformed to the time domain to provide an impulse response for the cable. For each distance, d, in the time domain an inverse Fourier transform to the frequency domain is performed while correcting each point based on the distance and frequency for that point. The corrected data is then Fourier transformed back to the time domain to present an impulse response for a lossless cable so that the significance of discontinuities may be readily observed.
The objects, advantages and other novel features of the present invention are apparent from the following detailed description when read in light of the appended claims and drawing.